Introduction

The unprecedented financial crisis of 2008 revealed the uncritical dependence
of the global financial community and, by extension, the economic system,
on the innovative risk-management formula of David
X. Li known as the Gaussian
Copula function -- subsequently described as "the secret fomula
that destroyed Wall Street".

The debate on climate change, informed by the report of the United Nations
Intergovernmental Panel on Climate Change, culminating in the United Nations
Climate Change Conference (Copenhagen, 2009), has essentially been based
on the Kaya
Identity. This is an equation, little known to climate debaters and
negotiators, relating factors that determine the level of human impact on
climate, in the form of emissions of the greenhouse gas carbon dioxide.

As metrics both formulae have been positioned, with little question, as
fundamental to global strategic initiatives. The first example indicates
the danger of such dependence. The second raises questions about the coherence
of the debate on climate change -- at a time when scientists are vigorously
claiming a global consensus on the matter. But of greater concern is the
possible existence of other such metrics which have been placed at the heart
of strategic initiatives -- unknown to those who might question this tendency
to single-metric dependence, the validity of the metric, or the use of other
such metrics as the basis for other vital strategies, whether now or in the
future.

Gaussian Copula: investment risk

The innovative formula of David
X. Li with regard to the Gaussian
Copula function is of interest since its successful use is alleged
to be at the root of the overconfidence of the global financial community
in taking the high orders of investment risk which led to the global financial
crisis of 2008, and its consequences. It is admirably described by Felix
Salmon (Recipe
for Disaster: the formula that killed Wall Street, Wired,
17.03, March 2009) -- or on the title page of the issue as The Secret
Formula that Destroyed Wall Street. As Li had indicated in 2005 "Very
few people understand the essence of the model" (Mark Whitehouse, Slices
of Risk, The Wall Street Journal, 12 September 2005).
A second description is offered by Kevin Drum (The
Gaussian Copula, Mother Jones, 24 February 2009).

Li's original paper (On
Default Correlation: A Copula Function Approach, Journal
of Fixed Income 9, 2000, pp. 43-54) was the first appearance of
the Gaussian Copula models for the pricing of collateralized
debt obligations (CDO's). This quickly became a tool for financial
institutions to correlate associations between multiple securities --
allowing CDOs to be accurately priced for a wide range of investments
that were previously too complex to price, such as mortgages. In this
respect they were at the core of the subprime crisis.

Expressed succinctly, the formula is:

An articulated expression of the formula is:

Gaussian
Copula

Pr = probability that any two potential sources of risk
(A and B)
in a proposed investment will both default

Φ2 =
couples the individual probabilities
associated with A and B

=

TA = amount of time between
now and when A may be expected to default

Φ-1 (FA(1)) = probability of
how long A is likely to survive before defaulting

TB = amount of time between
now and when B may be expected to default

Φ-1 (FB(1)) = probability of
how long B is likely to survive before defaulting

.

γ = correlation
parameter, reducing correlation to a single constant

Kaya Identity: emissions

The Kaya Identity was developed by Japanese energy economist Yoichi Kaya.
It is the subject of his book Environment, Energy, and Economy: strategies
for sustainability co-authored with Keiichi Yokobori as the output of
the Conference on Global Environment, Energy, and Economic Development
(1993 : Tokyo, Japan). It states that total emission level can
be expressed as the product of four inputs: population, GDP per capita, energy
use per unit of GDP, carbon emissions per unit of energy consumed. This equation
is very simple and tricky, as it can be reduced to only two terms, but it
is developed so that the carbon emission calculation becomes easy, as per
the available data, or generally in which format the data is available.

Kaya Identity

F = P*(G / P)*(E / G)*(F / E) = P*g*e*f

F = global CO2 emissions from human sources,

P = global population,

G = world GDP

g = (G/P) is global per-capita GDP,

E = global primary energy consumption and e=(E/G) is the energy
intensity of world GDP

The Kaya identity plays a core role in the development of future emissions
scenarios in the IPCC Special
Report on Emissions Scenarios prepared for the Third
Assessment Report (TAR) in 2001. The scenarios
set out a range of assumed conditions for future development of each of the
four inputs. Population growth projections are available independently from
demographic research; GDP per capita trends are available from economic statistics
and econometrics; similarly for energy intensity and emission levels. The
projected carbon emissions can drive carbon cycle and climate models to predict
future CO2 concentration and climate change.

The Kaya identity (Kaya, 1990) is a decomposition that
expresses the level of energy related CO2 emissions as the product of
four indicators: (1) carbon intensity (CO2 emissions per unit of total
primary energy supply (TPES)), (2) energy intensity (TPES per unit of
GDP), (3) gross domestic product per capita (GDP/cap) and (4) population.
The global average growth rate of CO2 emissions between 1970 and 2004
of 1.9% per year is the result of the following annual growth rates:
population 1.6%, GDP/cap12 1.8%, energy-intensity of -1.2% and
carbon-intensity -0.2% ....

At the global scale, declining carbon and energy intensities have been unable
to offset income effects and population growth and, consequently, carbon
emissions have risen....

The challenge - an absolute reduction of global GHG emissions - is
daunting. It presupposes a reduction of energy and carbon intensities at
a faster rate than income and population growth taken together. Admittedly,
there are many possible combinations of the four Kaya
identity components, but with the scope and legitimacy of
population control subject to ongoing debate, the remaining two technology-oriented
factors, energy and carbon intensities, have to bear the main burden....
[emphasis added]

With regard to the Kaya Identity, at the time of the Copenhagen negotiations
on climate change, might its discoverer, Yoichi Kaya, have echoed the words
of David Li regarding the Gaussian Copula before the financial crash of 2008: "Very
few people understand the essence of the model"?

Following the consequences of any "binding agreement" in Copenhagen,
as with the financial crisis, might there be occasion for an article entitled
something like Recipe
for Disaster: the formula that crashed the climate
-- or perhaps as The Secret
Formula that Destroyed the Global Climate?

Is the unquestioning global confidence in the Kaya Identity to be compared
with that in the Gaussian Copula -- notably in the light of the unprecedented
resources invested in each?

There is
now scientific evidence that a structural issue is indeed involved. The
theoretical origin of this evidence may be surprising to the economic or
financial community, although it wouldn't be such a surprise for
scientists familiar with natural ecosystems, thermodynamics, complexity
or information theory. The science that explains this issue rests on a
thermodynamic approach with deep historical roots in economics. In this
view, complex systems, such as ecosystems, living organisms, and economies
are all seen as matter-, energy-, and information-flow systems. For example,
the famous food chain is actually a matter/energy flow-network built of
complex relationships among organisms. Plants capture the sun's
energy with photosynthesis; animals eat the plants; species then eat each
another in a chain to top predator, only to have all organisms die, decompose,
and their energy/matter be recycled by bacteria. Similarly, economies are
circulation networks consisting of millions of businesses and billions
of customers exchanging different products and services, which when taken
as a whole, are supposed to meet the needs of all participants....

Consequently, as Goerner (1999) says about universality: 'all [flow]
systems, no matter how complex, fall into one of a few classes. All members
of a class share certain common patterns of behavior.' Similarly,
Cvitanovic explains: 'The wonderful thing about this universality
is that it does not matter much how close our equations are to the ones
chosen by nature, as long as the model is in the same universality class…as
the real system. This means that we can get the right physics out of very
crude models.' The existence of parallel patterns and dynamics
explains why similar energy flow concepts and analysis methods apply to
economic systems as well as natural ones....

Sustainability of a complex flow system can therefore be defined as the
optimal balance between efficiency and resilience of its network. With
these distinctions we are able to define and precisely
quantify a complex system's sustainability in a single metric. Indeed,
there is now a way of quantitatively measuring all the relevant components
separately: total throughput, efficiency, and resilience. Furthermore, the underlying
mathematics are well-behaved enough so that there exists only one single
maximum for a given network system....

It is critical to understand that the findings described so far arise
from the very structure of a complex network system, and therefore that
they remain valid for any complex network with a similar structure, regardless
of what is being processed in the system: It can be biomass in an ecosystem,
information in a biological system, electrons in an electrical power distribution
network, or money in an economic system. This is precisely
one of the strong points of using a web-like network approach instead of
machine-like metaphor.
[emphasis added]

symmetry: this may itself constitute a form of metric.
Given the beauty of symmetry as
an attractive indicator of truth (cf Ian Stewart, Why
Beauty Is Truth: the history of symmetry, 2007), and despite
the "monstrous" complexity
of the highest forms of symmetry (cf Mark Ronan, Symmetry
and the Monster: one of the greatest quests of mathematics, 2006),
it is possible that the governance challenges of "globalization" call
for a form of marriage between "beauty" and such a "monster" -- but of
a quite unexpected order of complexity. The significance of the Monster is
briefly well-summarized by Marcus
du Sautoy (Patterns
that Hold Secrets to the Universe) and in a more technical manner
by Richard E. Borcherds (What
is the Monster?Notices of the A.M.S., 2002). It is indeed
suspected that the Monster is built in some subtle way into the structure
of the universe -- the ultimate metric?

systems: the Viable
Systems Model (VSM) is a model of the organizational structure
of any viable or autonomous system organized
in such a way as to meet the demands of surviving in the changing environment,
namely through adaptive capacity. The model is an abstracted cybernetic
(regulation theory) description that is applicable to any organization
that is a viable system and capable of autonomy.

Secret formulae?

One concern is the extent to which any single metric might be elaborated
and used in secret for competitive advantage. This is evident in the approach
taken by institutions in developing formulae used in trading on the financial
markets. Such management of risk is similarly evident in gambling where gamblers
may each develop and use their own secret formula.

Variants of such secretive possibilities are evident in secret societies
organized to offer access progressively to deeper knowledge -- presumably
more integrative and singular -- through a succession of initiations.
It is however also the case that commercial barriers to access to copyrighted
publications may render "secret" to the majority the models they
articulate.

Another form of metric is that used for page
ranking of results
from a search engine query, such as with Google. This could prove to be of
increasing relevance in shaping global knowledge society through secret
rules for including, excluding or weighting certain results -- possibly under
commercial, religious, political or security pressures (as recently highlighted in debate over access to Google in China). According to
Wikipedia, a generic page rank equation is as follows: